Which graph represents the function?

Mathematics

1 answer:

nydimaria [60]3 years ago

7 0

Answer:

Top right graph.

Step-by-step explanation:

The graph of f(x) = x has a slope of 1, and is increasing to the right until the point where x = -1.

The graph of f(x) = -x has a slope of -1 decreasing to the right from the point where x = -1.

The clear small circle means that the point is not included in the function ( because of the '<' ).

The filled circle means it is included ( the '≥').

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For the polynomial function ƒ(x) = x4 − 12x3 + 46x2 − 60x + 25, find all local and global extrema.

rodikova [14]

$\bf f(x)=x^4-12x^3+46x^2-60x+25\\\\
-------------------------------\\\\
\cfrac{df}{dx}=4x^3-36x^2+92x-60\implies 0=4x^3-36x^2+92x-60
\\\\\\
0=x^3-9x^2+23x-15\impliedby \textit{doing some synthetic division with 5}
\\\\\\
0=(x^2-4x+3)(x-5)\implies 0=(x-3)(x-1)(x-5)\\\\
-------------------------------\\\\
\begin{cases}
f(1)=0\leftarrow minimum&1,0\\
f(3)=16\leftarrow maximum&3,16\\
f(5)=0\leftarrow minimum&5,0
\end{cases}\impliedby \textit{3 extrema, locals and globals}$